Inhalt

Zusammenfassung: We construct a series of new hyperbolic black hole solutions in
Einstein-Dilaton system and we apply holographic approach to investigate the
spherical Renyi entropy in various deformations. Especially, we introduce
various powers in the scalar potential for massive and massless scalar cases.
These scalar potentials correspond to deformation of dual CFTs. We make use of
a systematic way to generate numerical hyperbolic AdS black hole solutions.
Based on these solutions, we study the temperature dependent condensation of
dual operator of massive and massless scalar respectively. These condensations
show that there might be phase transitions in deformed CFTs. We also compare
free energy between hyperbolic black hole solutions and hyperbolic AdS-SW black
hole to judge phase transitions. In order to confirm the existence of phase
transitions, we turn on linear in-homogenous perturbation to test stability of
these hyperbolic AdS black holes. In this paper, we show how potential
parameters affect the stability of hyperbolic black holes in several specific
examples. For generic value of potential parameters, it needs further study to
see how the transition happens. Finally, we comment on these instabilities
associated with spherical Renyi entropy in dual deformed CFTs.